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En este trabajo se estudia la estabilidad de reguladores, con acciones proporcional y derivativa, que usan información visual para el control de posición de robots planos paralelos. Para esto, se hace una revisión bibliográfica breve de técnicas empleadas en esta clase de mecanismos, así como de técnicas empleadas en mecanismos de cadena cinemática abierta para asegurar estabilidad. Se presenta el análisis de estabilidad utilizando funciones de Lyapunov estrictas que junto con el empleo del segundo método de estabilidad de Lyapunov aseguran que los sistemas en lazo cerrado obtenidos sean asintóticamente estables en un punto de equilibrio, diferenciándose así de los análisis usuales donde se requieren funciones candidatas de Lyapunov especiales junto con teoremas de estabilidad global como el teorema de Barbashin-Krasovski o el principio de invariancia de La Salle. Los algoritmos de control visual propuestos, haciendo uso de estimación de velocidad a partir de mediciones de posición, calculan los pares necesarios en las articulaciones activas del robot paralelo para así poder mover el órgano terminal a la posición deseada. Finalmente, el desempeño del control propuesto se evalúa en un prototipo de laboratorio y se ilustran los correspondientes resultados experimentales.

Comúnmente, en el diseño y sintonización de leyes de control para aplicaciones fuera del ámbito académico, se suelen emplear criterios relacionados con la teoría de Lyapunov. Sin embargo, en algunas ocasiones este tipo de criterios no son los más convenientes, debido principalmente a la existencia de algunas dinámicas no modeladas de los sistemas bajo estudio. En este artículo se presenta un análisis riguroso para determinar la estabilización práctica de una clase de sistemas no lineales con dinámicas inciertas empleando funcionales de Lyapunov-Krasovskii que incluyen términos exponenciales. Derivado de este análisis, se establecen condiciones suficientes de estabilidad práctica dadas por desigualdades lineales matriciales (LMIs, por sus siglas en inglés), las cuales se emplean para el diseño y sintonización de leyes de control que cuentan con una acción retardada y una acción integral, con las cuales, se busca la atenuación del ruido y la reducción del error en estado estacionario. Para ilustrar la efectividad y aplicabilidad de los resultados obtenidos, se presentan simulaciones y experimentos sobre un helicóptero de tres grados de libertad (3-GDL).

In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

In this article, the analysis and implementation of an alternative Flat Filtering Control for a class of partially known fourth order flat systems is given. The Flat filtering control uses the cascade property of the system, which leads to a simplified control design in which high order time derivatives are algebraically simplified in terms of low order measurable states and the subsequent integral compensation. The control proposal is implemented and validated experimentally in a fourth order mechanical system (rotatory flexible joint) with accurate tracking results.

In the present contribution, the problem of establishing tuning rules to proportional retarded controller for LTI systems is addressed. Based on the D-decomposition methodology and σ-stability analysis, analytic conditions are determined on the parameters of a delayed controller that guarantee us that the system response reaches the maximal decay rate. The conditions presented in this paper are tested experimentally in tracking tasks of a flexible joint robotic arm.

In the present contribution, a methodology to solve the tracking control problem of robot manipulators through the use of a Proportional Retarded plus Gravity (PR+G) compensation scheme is presented. The main advantage of the proposal is to avoid the necessity of velocity measurements or their estimation, which is commonly used in most control schemes, such as the proportional derivative-type controllers or the computed torque control. The design of the PR+G controller is addressed via σ-stability analysis and its performance is tested in an experimental platform that consists of 2 degrees of the freedom robot manipulator. The proposed controller is compared with a classic proportional derivative plus gravity compensation scheme. The results are analyzed from a frequency perspective and measured by a quadratic error index.

The extended state observer (ESO) is a key component in any active disturbance rejection control (ADRC) scheme. Its discrete implementation is thus crucial in practical applications. In this paper, a discrete delta operator ESO is introduced and analyzed. As a starting point, a discrete shift operator ESO is used for transformation from continuous-time to delta operator discrete-time. A quantitative comparison between shift operator and delta operator ESOs (with different sampling time \(\varDelta \)[s]) is conducted here using a servomechanism system. The obtained numerical results show the proposed delta operator observer to work better than the shift operator observer in certain aspects.

This article deals with the control of a class of robotic systems with constant input time delay through the Active Disturbance Rejection paradigm, by means of Generalized Proportional Integral observers. The system is represented as a linear perturbed system, whose lumped disturbance input is estimated and then compensated by an Extended State Observer-Based Control, which is implemented on a predictor scheme for the time delay compensation. A complete Lyapunov Krasovskii functional was used to perform the stability analysis, leading to an ultimate bound trajectory tracking error. The proposal is tested and validated on a two degrees of freedom robotic manipulator.

This paper is concerned with the design and experimental assessment of, both, feedback linearization and sliding mode control techniques to the tracking trajectory problem of a flexible-joint robotic arm for a smooth rest to rest maneuver. The robust improvement of these controllers is analyzed by means of additional integral compensation, in which an alternative sliding surface was proposed for the control of the flexible arm. A feedback linearization of the nonlinear dynamic equation of the robot arm is computed in order to get a full-state non-linear feedback control law. On the other hand, it is proposed a second order sliding mode control with an integral term in the sliding surface, which improves the robustness of the controller sliding surface. Some experimental evaluations that include the addition of external unmodeled perturbations to test the enhancement of the robustness property show the improvements and effectiveness of the proposed control laws in disturbance rejection tasks. The controllers were implemented using exclusively position measurements and time derivatives approximations.